Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1307.4009 · Physical Review B

Quantum Monte Carlo calculation of the Fermi liquid parameters of the two-dimensional homogeneous electron gas

N. D. Drummond, Richard J. Needs

Published Jul 25, 2013• 11 citations
arXivHTMLPDF

Abstract

Fermi liquid theory is the basic paradigm within which we understand the normal behavior of interacting electron systems, but quantitative values for the parameters that occur in this theory are currently unknown in many important cases. One such case is the two-dimensional homogeneous electron gas (2D HEG), which is realized in a wide variety of semiconductor devices. We have used quantum Monte Carlo (QMC) methods to calculate the Landau interaction functions between pairs of quasiparticles. We use these to study the Fermi liquid parameters, finding that finite-size effects represent a serious obstacle to the direct determination of Fermi liquid parameters in QMC calculations. We have used QMC data in the literature for other properties of the 2D HEG to assemble a set of ``best available'' values for the Fermi liquid parameters.

DOI
10.1103/physrevb.88.035133

Related papers

Two-dimensional homogeneous electron gas with symmetric dual-gate screening: Exchange-correlation functional and other ground-state properties

Yiqi Yang, Yubo Yang, Kun Chen +2 more

The two-dimensional (2D) homogeneous electron gas (HEG) is a fundamental model in quantum many-body physics. It is important to theoretical and computational studies, where exchange-correlation energies computed in it serve as the foundation for density-functional calculations. It is also of direct relevance to a variety of experimental settings, especially with the rapid recent growth in 2D materials and moir\'e systems. In these experiments, metallic gates are often present, which screen the Coulomb interaction between electrons. The effect of the screening can qualitatively change the behavior of the 2D HEG, and requires accurate many-body computations to capture. In this paper, we perform state-of-the-art diffusion Monte Carlo (DMC) calculations in the 2D HEG subjected to symmetric dual-gate screening. We systematically compute the correlation energy across a range of densities and gate separations for both spin unpolarized and fully polarized systems. A global fit is obtained for the correlation energy, using these data and imposing various limiting behaviors obtained from perturbation analysis. The functional will allow density-functional calculations to be performed for a variety of realistic experimental setups, which can accurately account for the presence of gates. We also investigate how the gate screening affects the bulk modulus, pair correlation function, and the structure factor of the 2D HEG, which can potentially be probed in experiments.

arXiv:2410.07445•Physical review. B./Physical review. B•Jan 16, 2025•3 citations

Quantum Monte Carlo study of the ground state of the two-dimensional Fermi fluid

N. D. Drummond, Richard J. Needs

We have used the variational and diffusion quantum Monte Carlo methods to calculate the energy, pair-correlation function, static structure factor, and momentum density of the ground state of the two-dimensional (2D) homogeneous electron gas. We have used highly accurate Slater-Jastrow-backflow trial wave functions and twist averaging to reduce finite-size effects where applicable. We compare our results with others in the literature and construct a local-density-approximation exchange-correlation functional for 2D systems.

arXiv:1002.2122•Physical Review B•Feb 13, 2009•40 citations

Quantum Monte Carlo calculation of the Fermi-liquid parameters in the two-dimensional electron gas

Yongkyung Kwon, David M. Ceperley, Richard M. Martin

Excitations of the two-dimensional electron gas, including many-body effects, are calculated with a variational Monte Carlo method. Correlated sampling is introduced to calculate small energy differences between different excitations. The usual pair-product (Slater-Jastrow) trial wave function is found to lack certain correlations entirely so that backflow correlation is crucial. From the excitation energies calculated here, we determine Fermi-liquid parameters and related physical quantities such as the effective mass and the Land\'e g factor of the system. Our results for the effective mass are compared with previous analytic calculations.

Physical review. B, Condensed matter•Jul 15, 1994•131 citations

Quantum Monte Carlo study of the quasiparticle effective mass of the two-dimensional uniform electron liquid

Sam Azadi, N. D. Drummond, Alessandro Principi +2 more

The real-space variation quantum Monte Carlo (VMC) and diffusion quantum Monte Carlo (DMC) are used to calculate the energy bands and the effective mass of the paramagnetic and ferromagnetic two-dimensional uniform electron liquid (2D-UEL). The many-body finite-size errors are minimized by performing simulations for three system sizes with the number of electrons, N = 146 , 218, and 302, for paramagnetic and N = 91 , 139, and 151 for ferromagnetic systems. We consider 2D-UEL to be within the density range 1 ≤ r s ≤ 10 . The VMC and DMC results predict that the effective mass m * of the paramagnetic 2D-UEL at high density r s = 1 is very close to 1, suggesting that the effective mass renormalization due to electron-electron interaction is negligible. We find that m * of the paramagnetic 2D-UEL obtained by the VMC and DMC methods increases by r s but with different slopes. Our VMC and DMC results for ferromagnetic 2D-UEL indicate that m * decreases rapidly by reducing the density due to the strong suppression of the electron-electron interaction.

arXiv:2505.05879•Physical review. B./Physical review. B•Aug 8, 2025•3 citations

Application of quantum Monte Carlo methods to excitonic and electronic systems

Robert Lee

The work in this thesis is concerned with the application and development of quantum Monte Carlo (QMC) methods. We begin by proposing a technique to maximise the efficiency of the extrapolation of DMC results to zero time step, finding that a relative time step ratio of 1:4 is optimal. We discuss the post-processing of QMC data and the calculation of accurate error bars by reblocking, setting out criteria for the choice of block length. We then quantify the effects of uncertainty in the correlation length on estimated error bars, finding that the frequency of outliers is significantly increased for short runs. We then report QMC calculations of biexciton binding energies in bilayer systems. We have also calculated exciton-exciton interaction potentials, and radial distribution functions for electrons and holes in bound biexcitons. We find a larger region of biexciton stability than other recent work [C. Schindler and R. Zimmermann, Phys. Rev. B 78, 045313 (2008)]. We also find that individual excitons retain their identity in bound biexcitons for large layer separations. Finally, we give details of a QMC study of the one-dimensional homogeneous electron gas (1D HEG). We present calculations of the energy, pair correlation function, static structure factor (SSF), and momentum density (MD) for the 1D HEG. We observe peaks in the SSF at even-integer-multiples of the Fermi wave vector, which grow as the coupling is increased. Our MD results show an increase in the effective Fermi wave vector as the interaction strength is raised in the paramagnetic harmonic wire; this appears to be a result of the vanishing difference between the wave functions of the paramagnetic and ferromagnetic systems. We have extracted the Luttinger liquid exponent from our MDs by fitting to data around the Fermi wave vector, finding good agreement between the exponents of the ferromagnetic infinitely-thin and harmonic wires.

•Jul 12, 2011•1 citation

Ground-state properties of the one-dimensional electron liquid

R. M. Lee, N. D. Drummond

We present calculations of the energy, pair-correlation function (PCF), static structure factor (SSF), and momentum density (MD) for the one-dimensional electron gas using the quantum Monte Carlo method. We are able to resolve peaks in the SSF at even-integer multiples of the Fermi wave vector, which grow as the coupling is increased. Our MD results show an increase in the effective Fermi wave vector as the interaction strength is raised in the paramagnetic harmonic wire; this appears to be a result of the vanishing difference between the wave functions of the paramagnetic and ferromagnetic systems. We have extracted the Luttinger liquid exponent from our MDs by fitting to data around ${k}_{\mathrm{F}}$, finding good agreement between the exponent of the ferromagnetic infinitely thin wire and the ferromagnetic harmonic wire.

arXiv:1102.3854•Physical Review B•Jun 22, 2011•47 citations
Fermi liquid theory is the basic paradigm within which we understand the normal behavior of interacting electron systems, but quantitative values for the parameters that occur in this theory are currently unknown in many important cases. One such case is the two-dimensional homogeneous electron gas (2D HEG), which is realized in a wide variety of semiconductor devices. We have used quantum Monte Carlo (QMC) methods to calculate the Landau interaction functions between pairs of quasiparticles. We use these to study the Fermi liquid parameters, finding that finite-size effects represent a serious obstacle to the direct determination of Fermi liquid parameters in QMC calculations. We have used QMC data in the literature for other properties of the 2D HEG to assemble a set of ``best available'' values for the Fermi liquid parameters.
The two-dimensional (2D) homogeneous electron gas (HEG) is a fundamental model in quantum many-body physics. It is important to theoretical and computational studies, where exchange-correlation energies computed in it serve as the foundation for density-functional calculations. It is also of direct relevance to a variety of experimental settings, especially with the rapid recent growth in 2D materials and moir\'e systems. In these experiments, metallic gates are often present, which screen the Coulomb interaction between electrons. The effect of the screening can qualitatively change the behavior of the 2D HEG, and requires accurate many-body computations to capture. In this paper, we perform state-of-the-art diffusion Monte Carlo (DMC) calculations in the 2D HEG subjected to symmetric dual-gate screening. We systematically compute the correlation energy across a range of densities and gate separations for both spin unpolarized and fully polarized systems. A global fit is obtained for the correlation energy, using these data and imposing various limiting behaviors obtained from perturbation analysis. The functional will allow density-functional calculations to be performed for a variety of realistic experimental setups, which can accurately account for the presence of gates. We also investigate how the gate screening affects the bulk modulus, pair correlation function, and the structure factor of the 2D HEG, which can potentially be probed in experiments.
We have used the variational and diffusion quantum Monte Carlo methods to calculate the energy, pair-correlation function, static structure factor, and momentum density of the ground state of the two-dimensional (2D) homogeneous electron gas. We have used highly accurate Slater-Jastrow-backflow trial wave functions and twist averaging to reduce finite-size effects where applicable. We compare our results with others in the literature and construct a local-density-approximation exchange-correlation functional for 2D systems.
Excitations of the two-dimensional electron gas, including many-body effects, are calculated with a variational Monte Carlo method. Correlated sampling is introduced to calculate small energy differences between different excitations. The usual pair-product (Slater-Jastrow) trial wave function is found to lack certain correlations entirely so that backflow correlation is crucial. From the excitation energies calculated here, we determine Fermi-liquid parameters and related physical quantities such as the effective mass and the Land\'e g factor of the system. Our results for the effective mass are compared with previous analytic calculations.
The real-space variation quantum Monte Carlo (VMC) and diffusion quantum Monte Carlo (DMC) are used to calculate the energy bands and the effective mass of the paramagnetic and ferromagnetic two-dimensional uniform electron liquid (2D-UEL). The many-body finite-size errors are minimized by performing simulations for three system sizes with the number of electrons, N = 146 , 218, and 302, for paramagnetic and N = 91 , 139, and 151 for ferromagnetic systems. We consider 2D-UEL to be within the density range 1 ≤ r s ≤ 10 . The VMC and DMC results predict that the effective mass m * of the paramagnetic 2D-UEL at high density r s = 1 is very close to 1, suggesting that the effective mass renormalization due to electron-electron interaction is negligible. We find that m * of the paramagnetic 2D-UEL obtained by the VMC and DMC methods increases by r s but with different slopes. Our VMC and DMC results for ferromagnetic 2D-UEL indicate that m * decreases rapidly by reducing the density due to the strong suppression of the electron-electron interaction.
The work in this thesis is concerned with the application and development of quantum Monte Carlo (QMC) methods. We begin by proposing a technique to maximise the efficiency of the extrapolation of DMC results to zero time step, finding that a relative time step ratio of 1:4 is optimal. We discuss the post-processing of QMC data and the calculation of accurate error bars by reblocking, setting out criteria for the choice of block length. We then quantify the effects of uncertainty in the correlation length on estimated error bars, finding that the frequency of outliers is significantly increased for short runs. We then report QMC calculations of biexciton binding energies in bilayer systems. We have also calculated exciton-exciton interaction potentials, and radial distribution functions for electrons and holes in bound biexcitons. We find a larger region of biexciton stability than other recent work [C. Schindler and R. Zimmermann, Phys. Rev. B 78, 045313 (2008)]. We also find that individual excitons retain their identity in bound biexcitons for large layer separations. Finally, we give details of a QMC study of the one-dimensional homogeneous electron gas (1D HEG). We present calculations of the energy, pair correlation function, static structure factor (SSF), and momentum density (MD) for the 1D HEG. We observe peaks in the SSF at even-integer-multiples of the Fermi wave vector, which grow as the coupling is increased. Our MD results show an increase in the effective Fermi wave vector as the interaction strength is raised in the paramagnetic harmonic wire; this appears to be a result of the vanishing difference between the wave functions of the paramagnetic and ferromagnetic systems. We have extracted the Luttinger liquid exponent from our MDs by fitting to data around the Fermi wave vector, finding good agreement between the exponents of the ferromagnetic infinitely-thin and harmonic wires.
We present calculations of the energy, pair-correlation function (PCF), static structure factor (SSF), and momentum density (MD) for the one-dimensional electron gas using the quantum Monte Carlo method. We are able to resolve peaks in the SSF at even-integer multiples of the Fermi wave vector, which grow as the coupling is increased. Our MD results show an increase in the effective Fermi wave vector as the interaction strength is raised in the paramagnetic harmonic wire; this appears to be a result of the vanishing difference between the wave functions of the paramagnetic and ferromagnetic systems. We have extracted the Luttinger liquid exponent from our MDs by fitting to data around kF{k}_{\mathrm{F}}kF​, finding good agreement between the exponent of the ferromagnetic infinitely thin wire and the ferromagnetic harmonic wire.